Approximation of a compressible Navier-Stokes system by non-linear acoustical models

Anna Rozanova-Pierrat (1)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a com-pressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Anna Rozanova-Pierrat. Approximation of a compressible Navier-Stokes system by non-linear acoustical models. DAYS on DIFFRACTION 2015, May 2015, St. Petersburg, Russia. IEEE pp.270--276, 2015, Proceedings of the International Conference “Days on Diffraction 2015”, St. Petersburg, Russia, 978-1-4673-8630-2 ⟨10.1109/DD.2015.7354874⟩. ⟨hal-01257919⟩